Finite Group Databasebeta

← Group #10772463

Character table — Group #10772463

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666666644888888881212121212121212121212122424242424242424242424242424242444444444441212121212121212222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ91111-1-11-1-11-1-1111-1-1-1-1111-111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11-111-1-111-1-111-1-11-111-1-11-1
χ101111-1-11-1-11-1-1111-1-1-1-1111-111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-111-11-1-111-11
χ111111-1-11-1-11-1-1111-1-1-1-1111-111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-1111-11-1-1111-1-1-11
χ121111-1-11-1-11-1-1111-1-1-1-1111-111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-1-111-1-111-11-111-1-1-1111-1
χ131111-1-11-1-11-1-1111-1-1-1-1111-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1111-1-1-1-11111-1-11-1-1-111-11
χ141111-1-11-1-11-1-1111-1-1-1-1111-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1111-1-1-1-111-1-111-1111-1-11-1
χ151111-1-11-1-11-1-1111-1-1-1-1111-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-1-11111-1-11-11-1-11-1-1111-1
χ161111-1-11-1-11-1-1111-1-1-1-1111-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1-11111-1-1-11-111-111-1-1-11
χ17222222222-2-2-2-2-2-22222222-2200000000-2-2-2-2-2-222-2-22200000000000000002-22-20000002-22-20000000000000000
χ18222222222-2-2-2-2-2-22222222-2200000000-2-2-2-2-2-222-2-2220000000000000000-22-22000000-22-220000000000000000
χ192222222-2-2222-2-222222222-2-200000000-2-2-2-222-2-222-2-20000000000000000000022220000000000-200-200000000
χ202222222-2-2222-2-222222222-2-200000000-2-2-2-222-2-222-2-200000000000000000000-2-2-2-20000000000200200000000
χ212222222-2-2-2-2-222-222222222-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000000002-20-22000000
χ222222222-2-2-2-2-222-222222222-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000000-2202-2000000
χ23222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-1-1-11111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000221111-1-1-1-1000000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000111111-1-111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-2000000-11-11−i3i3−i3i3000000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000111111-1-111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-220000001-11-1i3−i3i3−i3000000000000
χ29222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000111111-1-111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-2000000-11-11i3−i3i3−i3000000000000
χ30222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000111111-1-111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-220000001-11-1−i3i3−i3i3000000000000
χ312222-2-22222-2-2-2-22-2-2-2-22222-200000000-2-2222222-2-2-2-20000000000000000000022-2-20000000000-200200000000
χ322222-2-22222-2-2-2-22-2-2-2-22222-200000000-2-2222222-2-2-2-200000000000000000000-2-2220000000000200-200000000
χ332222-2-2222-22222-2-2-2-2-2222-2-20000000022-2-2-2-22222-2-200000000000000000000000000000000000220-2-2000000
χ342222-2-2222-22222-2-2-2-2-2222-2-20000000022-2-2-2-22222-2-200000000000000000000000000000000000-2-2022000000
χ352222-2-22-2-2-222-2-2-2-2-2-2-22222200000000-2-222-2-2-2-2222200000000000000002-2-220000002-2-220000000000000000
χ362222-2-22-2-2-222-2-2-2-2-2-2-22222200000000-2-222-2-2-2-222220000000000000000-222-2000000-222-20000000000000000
χ372222-2-2-1-2-22-2-22221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-111-1-111000000000000
χ382222-2-2-1-2-22-2-22221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-111-1-1000000000000
χ392222-2-2-1-2-22-2-22221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ402222-2-2-1-2-22-2-22221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ412222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-22000000-111-1−i3i3i3−i3000000000000
χ422222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-20000001-1-11i3−i3−i3i3000000000000
χ432222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-22000000-111-1i3−i3−i3i3000000000000
χ442222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-20000001-1-11−i3i3i3−i3000000000000
χ452-2-222-220022-200-222-2-2-22-200−i2−i2i2i2−i2−i2i2i200002-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i00000000000000002−22−200
χ462-2-222-220022-200-222-2-2-22-200−i2−i2i2i2−i2−i2i2i200002-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i0000000000000000−22−2200
χ472-2-222-220022-200-222-2-2-22-200i2i2−i2−i2i2i2−i2−i200002-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i0000000000000000−22−2200
χ482-2-222-220022-200-222-2-2-22-200i2i2−i2−i2i2i2−i2−i200002-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i00000000000000002−22−200
χ492-2-22-222002-2200-2-2-222-22-200−i2−i2i2i2i2i2−i2−i200002-200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i00000000000000002−2−2200
χ502-2-22-222002-2200-2-2-222-22-200−i2−i2i2i2i2i2−i2−i200002-200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i0000000000000000−222−200
χ512-2-22-222002-2200-2-2-222-22-200i2i2−i2−i2−i2−i2i2i200002-200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i0000000000000000−222−200
χ522-2-22-222002-2200-2-2-222-22-200i2i2−i2−i2−i2−i2i2i200002-200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i00000000000000002−2−2200
χ53444444-2-4-4444-4-44-2-2-2-2-2-2-2-4-4000000002222-2-222-2-2220000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-444-4-2-2-2-2-2-2-24-400000000-2-2-2-2222222220000000000000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-442222-2-2-24-40000000022-2-2-2-2-2-222220000000000000000000000000000000000000000000000
χ564444-4-4-244-44444-42222-2-2-2-4-400000000-2-22222-2-2-2-2220000000000000000000000000000000000000000000000
χ5744-4-4004000004-4000004-4-400000022−2222−224-400000000000000000022−2222−2222−2222−22000000000000000000000000000000
χ5844-4-4004000004-4000004-4-4000000−2222−22224-4000000000000000000−2222−2222−2222−2222000000000000000000000000000000
χ5944-4-400400000-44000004-4-40022−2222−220000-44000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ6044-4-400400000-44000004-4-400−2222−22220000-440000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ6144-4-400-2000004-40−2i32i3−2i32i3-22200000022−2222−22-22−2i32i300000000i6−i6i6−i6−i6i6−i6i6−22−22−22−22000000000000000000000000000000
χ6244-4-400-2000004-40−2i32i3−2i32i3-222000000−2222−2222-22−2i32i300000000−i6i6−i6i6i6−i6i6−i62−22−22−22−2000000000000000000000000000000
χ6344-4-400-2000004-402i3−2i32i3−2i3-22200000022−2222−22-222i3−2i300000000−i6i6−i6i6i6−i6i6−i6−22−22−22−22000000000000000000000000000000
χ6444-4-400-2000004-402i3−2i32i3−2i3-222000000−2222−2222-222i3−2i300000000i6−i6i6−i6−i6i6−i6i62−22−22−22−2000000000000000000000000000000
χ6544-4-400-200000-440−2i32i3−2i32i3-2220022−2222−2200002-22i3−2i300000000−22−22−22−22i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ6644-4-400-200000-440−2i32i3−2i32i3-22200−2222−222200002-22i3−2i3000000002−22−22−22−2−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ6744-4-400-200000-4402i3−2i32i3−2i3-2220022−2222−2200002-2−2i32i300000000−22−22−22−22−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ6844-4-400-200000-4402i3−2i32i3−2i3-22200−2222−222200002-2−2i32i3000000002−22−22−22−2i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ694-44-40044-40000000000-4-44002i−2i−2i2i2i−2i−2i2i0000004-400002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ704-44-40044-40000000000-4-4400−2i2i2i−2i−2i2i2i−2i0000004-40000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-44-4004-440000000000-4-44002i−2i−2i2i−2i2i2i−2i000000-4400002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-44-4004-440000000000-4-4400−2i2i2i−2i2i−2i−2i2i000000-440000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-44-400-24-4000000−2i32i32i3−2i322-2002i−2i−2i2i2i−2i−2i2i000000-2200−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000000000
χ744-44-400-24-4000000−2i32i32i3−2i322-200−2i2i2i−2i−2i2i2i−2i000000-2200−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000000000
χ754-44-400-24-40000002i3−2i3−2i32i322-2002i−2i−2i2i2i−2i−2i2i000000-22002i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000000000
χ764-44-400-24-40000002i3−2i3−2i32i322-200−2i2i2i−2i−2i2i2i−2i000000-22002i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000000000
χ774-44-400-2-44000000−2i32i32i3−2i322-2002i−2i−2i2i−2i2i2i−2i0000002-2002i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000000000
χ784-44-400-2-44000000−2i32i32i3−2i322-200−2i2i2i−2i2i−2i−2i2i0000002-2002i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000000000
χ794-44-400-2-440000002i3−2i3−2i32i322-2002i−2i−2i2i−2i2i2i−2i0000002-200−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000000000
χ804-44-400-2-440000002i3−2i3−2i32i322-200−2i2i2i−2i2i−2i−2i2i0000002-200−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000000000
χ814-4-444-4400-4-4400444-4-4-44-400000000000000-4400-44000000000000000000000000000000000000000000000000
χ824-4-444-4-20044-400-4-2-2222-2200−2i2−2i22i22i2−2i2−2i22i22i20000-2200-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000
χ834-4-444-4-20044-400-4-2-2222-22002i22i2−2i2−2i22i22i2−2i2−2i20000-2200-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000
χ844-4-444-4-200-4-44004-2-2222-22000000000000002-2002-20066−6−6−6−66666−6−6−6−666000000000000000000000000000000
χ854-4-444-4-200-4-44004-2-2222-22000000000000002-2002-200−6−66666−6−6−6−66666−6−6000000000000000000000000000000
χ864-4-44-44400-44-4004-4-444-44-400000000000000-44004-4000000000000000000000000000000000000000000000000
χ874-4-44-44-2004-4400-422-2-22-2200−2i2−2i22i22i22i22i2−2i2−2i20000-22002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000
χ884-4-44-44-2004-4400-422-2-22-22002i22i2−2i2−2i2−2i2−2i22i22i20000-22002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000
χ894-4-44-44-200-44-400422-2-22-22000000000000002-200-220066−6−6−6−666−6−66666−6−6000000000000000000000000000000
χ904-4-44-44-200-44-400422-2-22-22000000000000002-200-2200−6−66666−6−666−6−6−6−666000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.